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The smoothness of the material functions, provided here by the smoothness of the defining function for the shape, helps to avoid undesirable singularities in the material distribution, like stress or concentrations. We illustrate application of the SARDF operations by two- and three-dimensional heterogeneous object modeling case studies.<\/jats:p>","DOI":"10.1115\/1.2218366","type":"journal-article","created":{"date-parts":[[2006,8,16]],"date-time":"2006-08-16T22:02:41Z","timestamp":1155765761000},"page":"221-229","update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":10,"title":["Constructive Heterogeneous Object Modeling Using Signed Approximate Real Distance Functions"],"prefix":"10.1115","volume":"6","author":[{"given":"Pierre-Alain","family":"Fayolle","sequence":"first","affiliation":[{"name":"The University of Aizu , Department of Information Systems, Tsuruga, Ikki-Machi, Aizu-Wakamatsu City, Fukushima, 965-8580, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Pasko","sequence":"additional","affiliation":[{"name":"Hosei University , 3-7-2 Kajino-cho, Koganei-shi, Tokyo 184-8584, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjamin","family":"Schmitt","sequence":"additional","affiliation":[{"name":"Computer Graphics Research Institute and Hosei University , Digital Media Professional, Mitaka takagi Building, 1-15-5 Nakacho, Musashino-shi, Tokyo 180-0006, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikolay","family":"Mirenkov","sequence":"additional","affiliation":[{"name":"The University of Aizu , Department of Information Systems, Tsuruga, Ikki-Machi, Aizu-Wakamatsu City, Fukushima, 965-8580, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2005,11,25]]},"reference":[{"issue":"2","key":"2022060612261690300_c1","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1093\/comjnl\/16.2.157","article-title":"A Constructive Geometry for Computer Graphics","volume":"16","author":"Ricci","journal-title":"Comput. 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